Problem: Simplify the following expression: $y = \dfrac{-3r^2 + 21r - 36}{r - 3} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-3$ , so we can rewrite the expression: $ y =\dfrac{-3(r^2 - 7r + 12)}{r - 3} $ Then we factor the remaining polynomial: $r^2 {-7}r + {12} $ ${-3} {-4} = {-7}$ ${-3} \times {-4} = {12}$ $ (r {-3}) (r {-4}) $ This gives us a factored expression: $\dfrac{-3(r {-3}) (r {-4})}{r - 3}$ We can divide the numerator and denominator by $(r + 3)$ on condition that $r \neq 3$ Therefore $y = -3(r - 4); r \neq 3$